Is it theoretically possible to alter a burned-in NIC MAC address permanently?

Not spoofing, but change the MAC address on the read-only firmware on the hardware itself by somehow hacking it so that if the default NIC is loaded on any computer or any OS, the MAC address will report the altered address instead of the burned-in one.

I'm not sure how I can describe what I'm trying to ask more specifically...

Like, changing the MAC address on a networking card in a way such that if you remove the networking card from the computer and install the (unaltered) driver for it (that is used universally for that particular card on a given OS) on another random computer, that random machine would recognize the network card's MAC as the one you changed it to. Something like that.